Question 8.2.17: Show that, if X ≥ 0, then P(X ≥ a) ≤ E(X)/a....
Show that, if X ≥ 0, then P(X ≥ a) ≤ E(X)/a.
E(X) =ʃ∞−∞ xp(x)dx. Since X is non-negative, we have
E(X)\geq \int_{x\geq a}^{}{xp(x)dx}\geq aP(X\geq a).
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